The navigation signals from Global Navigation Satellite Systems (GNSS), such as the Global Positioning System (GPS) and GLONASS, are used by GNSS receivers to provide position, navigations and timing (PNT) services, and many related applications.
As shown in FIG. 1, a GNSS receiver (110) typically comprises a radio frequency (RF) section (102) and a digital section (105). The digital section (105) further comprises a central processing unit (CPU) (107) and a memory (104). Some GNSS receivers share the digital section with a host device, such as a cell phone, or a personal navigation device.
To perform its basic positioning function, which underlies nearly all PNT applications, a GNSS receiver first acquires the GNSS navigation signal (101) from a sufficient number of GNSS satellites (100), and then extracts from the signal (101) the necessary navigation information. The acquisition of the GNSS signal is carried out in the RF section (102), and the extraction of the navigation information is carried out in the digital section (105). The navigation information embedded in the GNSS navigation signal, and required for positioning, comprises i) the range from the receiver to the transmitting satellites (also known as Pseudo Range because it depends on the inaccurate knowledge of the satellite and receiver clocks, which must later be adjusted using information about the GNSS satellite clock states from the broadcast navigation message, and a least squares estimation of the receiver clock state), and ii) the location, velocity, and clock state of the transmitting satellites. Using data i) and ii), the receiver can triangulate its position using a least squares or similar estimation approach.
An important metric of receiver performance is the time to first fix (TTFF). This metric measures how long it takes a receiver to acquire the GNSS signals and estimate its position under a variety of conditions, including cold start, i.e., in the absence of any prior accurate knowledge of its position or time or of the current state of the GNSS satellites. For best user experience it is desirable that TTFF be minimized. A significant portion of TTFF from cold start (or even from ‘warm start’, where partial relevant a priori information is available) is spent by the receiver's RF section (102) in acquiring the GNSS signals, and an additional time is spent in the digital section (105) in extracting the satellite position and clock state information from the navigation message portion of the GNSS navigation signal.
The time-consuming aspect of the signal acquisition stems from the need to scan the full possible space of range and Doppler values for the desirable signal. The actual speed with which any particular GNSS receiver acquires the GNSS navigation signals strongly depends on its design, its location and its environment.
After the signals have been acquired by the RF section (102), the navigation information has to be extracted in another time-consuming step. For example, the GPS navigation message is encoded as a 50 bits per second binary data stream, and the precise broadcast ephemeris data containing the needed information about the satellite orbit and clock states are spread over a 1500-bit frame (sequence of bits), requiring the receiver (110) to spend up to 30 seconds to extract all the necessary broadcast ephemeris information.
The common approaches to reduce TTFF for GNSS receivers revolve around ‘aiding’ the receiver with external information. Such information typically takes the form of expected orbit and clock states for the GNSS satellites. With additional a priori information, crude as it may be, of its position and/or clock state, the receiver can narrow the search range and Doppler search space for the GNSS signals and acquire them more quickly. If the aided GNSS orbit and clock states (together called the satellite ephemerides) thus provided to the receiver are sufficiently accurate, they can obviate the need to extract the equivalent information from the navigation signal, further reducing TTFF.
Two basic approaches have been employed for the provision of this type of aid to the receiver (110). The first approach is to provide the receiver (110) in near-real-time with the GNSS orbit and clock states as they are being observed concurrently by a neighboring receiver, or by a network of receivers. This approach requires a continuous, low-latency communications channel, with a fairly high bandwidth, between the monitoring receiver(s), a sequence of servers to collect, process, and disseminate the useful information, and the targeted receiver, which could be, for example, a cell phone or a car navigation device anywhere in the word, or a satellite in low Earth orbit. The second approach being employed is to periodically transfer to the targeted receiver a set of orbit and clock states for the GNSS satellites that are valid over an extended period of time into the future, thus reducing the demands on the required external communications channels. These extended orbit and clock states are calculated by external servers using the broadcast ephemeris and/or range measurements collected over time from a network of GNSS tracking receivers. This latter approach was employed by JPL as early as 1992 in aiding the GPS receiver on the Topex satellite reduce its TTFF. This approach is predicated on the ability to predict, or extend, the GNSS orbit and clock states into the future from past or current information. These ephemerides (comprising the orbit and clock states) are known as ‘predicted’ or ‘extended’ ephemerides. In a variant of the latter approach, a server periodically calculates the initial conditions, or ‘seeds’ of the extended orbit and clock states, and sends only these seeds to the receiver, reducing the needed communications bandwidth. The receiver then generates the extended ephemeris from the seeds using a stored model of the satellite orbit and clock dynamics.
Regardless of the aiding approach, whether with near-real-time ephemeris or related information (such as the full GNSS navigation message), or with extended ephemeris or related information (such as seeds for an extended ephemeris model), they all require a considerable external infrastructure including a network of tracking receivers, servers, and some sort of communications channels between the targeted receiver and the servers of the aiding information. All of these must operate continuously and reliably, and incur significant cost for equipment, real-estate, communications fees, and human monitoring and maintenance.
The trajectory of GNSS satellites, such as GPS and GLONASS, is affected by many physical factors which are not perfectly known, or that are not completely predictable, such as the gravitational attraction of the Earth and the flux of the solar radiation. It is therefore difficult to predict the trajectory of these satellites into the future, and invariably, the accuracy of such predictions degrades with time. It is even harder to predict the state of the atomic clocks on these satellites, as they are subject to both random processes and complex environmental effects (temperature, for example). In addition, the satellites' trajectories and clock states can occasionally be altered by their operators, rendering useless any orbit and clock state prediction. For these reasons, the predicted ephemeris must be updated periodically at fairly regular intervals. These intervals are typically governed by the quality of the satellite clock prediction (which is the quantity hardest to predict), and usually varies from sub-daily to weekly, depending on the receiver's positioning accuracy requirements, and the quality of the orbit and clock prediction algorithms.
There are two basic approaches for predicting the orbit and clock states. The least accurate approach is to obtain a satellite state (orbit and clock) representation at a given time, and propagate it forward with an a priori model. A second, more accurate approach, uses a time series of the satellite or clock states and fits to it a set of model parameters. For the orbit, these model parameters include three initial position coordinates, three initial velocity coordinates, and several physical and empirical parameters of the satellite dynamics, such as solar pressure scale, and constant accelerations. Once these model parameters are estimated, the model can be propagated numerically forward, yielding higher fidelity predicted orbits. A similar process is followed to optimize clock prediction. The time series of orbit and clock states to which the model parameters are fit could be based on accurate data as obtained, for example, from a network-based GNSS orbit determination, or on less accurate data obtained, for example, from the broadcast ephemerides. Regardless, the dominant error source in GNSS orbit and clock predictions is due to uncertainty in the propagation model. The accuracy of the source for the data to fit, whether the broadcast ephemerides or precise ephemerides, is relatively unimportant.
The physical models governing the motion of satellites are best described in a coordinate system that is fixed in inertial space (Earth-centered-inertial—ECI). Consequently, orbit propagation for GNSS satellites is carried out in an ECI coordinate system. However, a terrestrial GNSS receiver requires position information in a coordinate system rotating with the Earth (Earth-centered-Earth-fixed—ECEF), as indeed provided by the GNSS broadcast ephemeris. Therefore, the predicted orbit should be transformed from ECI to ECEF coordinates before it can be used for receiver aiding, and this requires the knowledge of the Earth orientation in inertial space at any given time. However, the Earth orientation follows a highly complex and unpredictable pattern. Earth orientation is observed and reported after elaborate data processing operations using the geodetic techniques of Very Long Baseline Interferometry (VLBI), and GPS. The three key Earth orientation model parameters (EOP), X and Y polar motion, and Length of Day (LOD) are reported periodically by a few agencies, such as NASA-JPL, the International Earth Rotation and Reference Systems Service (IERS), or the National Geo-spatial Agency (NGA), and are used universally to describe the Earth orientation, and enable the transformation between ECI and ECEF coordinate systems. The dependency on these external sources of periodic Earth orientation is currently one of the insurmountable obstacles to accurate, long-term, in-receiver autonomous ephemeris prediction and aiding.